Hundreds of Syrian rebel fighters began a process of leaving the besieged Damascus suburb of Barzeh on Monday as part of an evacuation deal agreed with the government, state television and a war monitor reported.

State-run Ekhbariya television cited its reporter there as saying the evacuation of fighters from Barzeh for the rebel-held Idlib province in northwest Syria had begun to be implemented but without giving further details.

The Syrian Observatory for Human Rights, a Britain-based war monitor, reported that buses had arrived in Barzeh at dawn and a group of hundreds of fighters and their family members had started to board them.

The Observatory said more people would leave Barzeh over the coming days as part of the same deal.

Barzeh is in northeast Damascus near the rebel-held Eastern Ghouta oasis district of towns and farms and has been the site of intense fighting between insurgents and the Syrian army in recent months.

On Sunday, the army advanced under intense bombardment in the Qaboun district, which adjoins Barzeh in the same besieged enclave, the Observatory said.

A military media unit run by the armed Lebanese Shi'ite group Hezbollah, an ally of the Syrian government, reported on Monday that several Red Crescent ambulances had also arrived at the rebel-besieged towns of al-Foua and Kefraya near Idlib.

Those two towns were part of a mutual evacuation deal that also included two towns besieged by government forces and involved exchanging thousands of people between the warring sides last month.

Syrian President Bashar Assad has promoted the use of such evacuations, along with what his government calls "reconciliation" deals for rebel-held areas that surrender to the government, as a way of reducing bloodshed.

However, the United Nations has criticized both the use of siege tactics which precede such deals and the evacuations themselves as amounting to forcible displacement.

Many of those who have left other besieged areas of Syria have also relocated to Idlib, a mostly rural province abutting the Turkish border which is a major rebel stronghold.